Related papers: High Dimensional Expanders: Eigenstripping, Pseudo…
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally they show that there cannot be too many eigenvalues near the…
We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with…
In two recent works, Hoffman, Johnson and Junge proved the density conjecture, the hockey stick conjecture and the ball conjecture for Activated Random Walks in dimension one, showing an equality between several different definitions of the…
The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner.…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
In this paper we construct uniformly expanding random walks on smooth manifolds. In higher dimensions, our definition of uniform expansion measures the growth of subspaces rather than single vectors. Potrie showed that given any open set…
We consider random walks on comb- and brush-like graphs consisting of a base (of fractal dimension $D$) decorated with attached side-groups. The graphs are also characterized by the fractal dimension $D_a$ of a set of anchor points where…
We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non-existence of moments for first-passage and last-exit times. In our…
We revisit the multifractal analysis of $\R^d$-valued branching random walks averages by considering subsets of full Hausdorff dimension of the standard level sets, over each infinite branch of which a quantified version of the…
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…
Discrete time random walks, in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$, are widely used models for stochastic processes. In the case of a correlated random walk, the next…
We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…
In this work we show that high dimensional expansion implies locally testable code. Specifically, we define a notion that we call high-dimensional-expanding-system (HDE-system). This is a set system defined by incidence relations with…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to…
We propose random walks on suitably defined graphs as a framework for finescale modeling of particle motion in an obstructed environment where the particle may have interactions with the obstructions and the mean path length of the particle…
This work extends Roberts et al. (1997) by considering limits of Random Walk Metropolis (RWM) applied to block IID target distributions, with corresponding block-independent proposals. The extension verifies the robustness of the optimal…
We consider the problem of approximately solving constraint satisfaction problems with arity $k > 2$ ($k$-CSPs) on instances satisfying certain expansion properties, when viewed as hypergraphs. Random instances of $k$-CSPs, which are also…
For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states that $\lambda(G) \leq h(G)$, where…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…